Elements which are present in atomic state emit, when they are excited, the line spectrum of the atoms. Depending on the nature of the excitation by means of an inductively coupled plasma, there are also observed from many elements the emission spectra originating from ions, i.e. ionized atoms. For reasons of simplicity, reference will be made hereinafter to atomic spectra which term will be understood to encompass the emission spectra of atoms as well as ions. Each element provides a line spectrum which is characteristic of this element. In such a line spectrum there are strong spectral lines, i.e. spectral lines having a high intensity, and less strong or weaker spectral lines. The intensity of the spectrum depends on the number of excited atoms in the light source. The spectral lines are very narrow and have a width of a few picometers.
It is known to introduce a sample solution which is to be analyzed into a plasma heated by high frequency and, for determining the concentration, to measure the intensities of certain spectral lines which are characteristic of different looked-for elements. A light beam originating from the plasma is spectrally dispersed by a spectrometer by means of a monochromator and the light intensity is measured as a function of wavelength using light-sensitive detector means. The detector means produce signals at the aforementioned characteristic spectral lines originating from the various looked-for elements. After corresponding calibration, the concentration of the individual elements can be determined from these signals.
In addition to the spectral lines of the different elements, there occurs a non-specific background emission. This background emission can depend on the wavelengths and can be structured.
In some cases, the spectral lines of different elements overlap. It is then difficult to determine the concentrations of such overlapping spectral lines.
In a publication by S. D. Brown "The Kalman Filter in "Analytical Chemistry" from "Analytica Chimica Acta", 181 (1986), 1-26 it is known to use Kalman filters for separating the overlapping signals of analyzing apparatus or for the drift compensation. It is mentioned that the condition variables can also be dependent on the wavelength instead of on the time. Algorithms used in the recursive, discrete Kalman filter are also described. In every recursion step an estimate of the condition vector is described. In the subsequent recursion step, a vector of a measurable variable or variables is measured. From a measuring matrix it is calculated which vector of measurable values, according to the estimate determined in the preceding recursion step, is to be predicted. The estimate of the condition vector is corrected by the difference between the measurable variables and the predicted measurable variables multiplied by a filter amplification. In this publication the possibility is also pointed out that the measuring matrix consists of several column vectors, each of which is a complete, visible spectrum as a consequence of molar absorption abilities. This measuring matrix interrelates the absorbency values measured with different wavelengths and the conditions of the filter, which can be stated as concentrations of the components. The filter model which is used is made from experimentally obtained signals from the analyzing apparatus. A filter with such empiric signals can serve for the easy resolution of overlapping spectra, i.e. absorption spectra.
A publication by T. F. Brown and S. D. Brown "Resolution of Overlapped Electrochemical Peaks with the Use of the Kalman Filter" in Analytical Chemistry" vol. 53 (1981), 1410-1417, describes the separation of overlapping electrochemical peaks by means of the Kalman filter. Also, curves with standard solutions of different elements are recorded. From these curves a model for a Kalman filter is formed. In this publication there is also described an innovation sequence as well as the displacement between sample spectra and model spectra by means of an iterative procedure.
A publication by G. H. Webster, T. L. Cecil and S. C. Rutan "Characterization of the Effect of Peak Shifts on the Performance of the Kalman Filter in Multicomponent Analysis" in "Journal of Chemometrics" vol. 3 (1988), 21-32 describes fluorescence analysis. However, in fluorescence analysis, problems occur in that the fluorophores are sensitive to the polarity of the vicinity. Thereby a spectral shift of the fluorescence emission spectrum by some nanometers can be effected. This publication also contains an indication of the magnitude of the covariance P and the variance of the noise in the measurement (S.sub.x.sup.2).
Also in this publication, the Kalman filter serves for the separation of overlapping spectra. The publication concerns the influence of peak shifts on the performance of the algorithms of a multi-component analysis with a Kalman filter. It is shown that the course of the difference between the actually measured measurable variable and the measurable variable predicted by the filter provides a measure for the amount and direction of the peak shift.
A publication of H. N. J. Poulisse and P. Engelen "The Kalman Filters as an On-line Drift Compensator in Multicomponent Analysis Determinations" in "Analytical Letters" 13(A14) (1980), 1211-1234 describes the compensation of a baseline drift in an analyzing apparatus by means of the Kalman filter. In the condition vector which is substantially formed by two concentrations, two different elements are provided with one being a factor multiplied by the running number and the other one being a constant. These two values are drift parameters which are provided by the Kalman filter.